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        <td class="header">&nbsp; Range Filtering (InSAR operator)</td>
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<h3>Range Filtering</h3>

<p>
    This operator filters the spectras, of stack of SLC images, in the range direction. This is an
    optional step in interferometric processing chain.
    The filtering in range direction of master and slave image increases Signal-to-Noise Ration (SNR) in the
    interferogram.
    This noise reduction results from filtering out non overlapping parts of the spectrum.
    This spectral non overlap in range between master and slave is caused by a slightly different viewing angle of both
    sensors. The longer the perpendicular baseline, the smaller the overlapping part. Eventually
    a baseline of about 1100 m results in no overlap at all (that is also critical
    baseline for ERS). Assuming no local terrain slope, a reduction of typically 10-20% in the number of residues can be
    achieved.
</p>

<p>
    The range filtering should be performed after coregistration (after slave images
    are resampled/warped to the master grid), because the fringe frequency is estimated from the interferogram (that is
    temporary computed). It is performed simultaneously for the master and slave image, unless there are multiple slave
    images in the stack. If later is the case, as with Azimuth Filtering Operator, only slave images will be filtered
    while the master image will be left in its original state.
</p>

<h4>Implementation Details</h4>

<p>
    Currently, only a so-called "adaptive" filtering is implemented, while method based on orbital data and terrain
    slope will be implemented in coming releases.
</p>

<p>
    Adaptive range filtering algorithm builds on the local fringe frequency estimated from the locally computed
    interferogram. After the warping/resampling of the slave on the master grid the local fringe frequency is
    estimated using peak analysis of the power of the spectrum of the complex interferogram. The warping/resampling
    is required since the local fringe frequency is estimated from the interferogram. The fringe frequency is
    directly related to the spectral shift in range direction. (Note: that this shift is not an actual shift, but
    it is an indication that the different frequencies are mapped on places with this shift.
</p>

<h4>Input parameters</h4>

<ul>
    <li>
        <b>FFT Window Length:</b> Length of the estimation window, a peak is estimated for parts of this length.
    </li>
    <!--<li>-->
        <!--<b>Range Filter Overlap:</b> Overlap between tiles in range direction.-->
    <!--</li>-->
    <li>
        <b>Hamming Alpha:</b> Weight for hamming filter. (Note that, if alpha is set to 1, the weighting window function will
        be of rectangular type).
    </li>
    <li>
        <b>Walking Mean Window:</b> Number of lines over which the (walking) mean will be computed. This parameter reduces
        noise for the peak estimation. The parameter has to be an odd number. Logically, the walking mean can be
        compared with the principles of periodogram estimation.
    </li>
    <li>
        <b>SNR Threshold:</b> In peak estimation, weight values to bias higher frequencies. The reasoning for this parameter is
        that the low frequencies are (for small Oversample factors) aliased after interferogram generation. The
        de-weighting is done by a dividing by a triangle function (convolution of 2 rect window functions,  the shape of
        the range spectrum). Effect of this parameter may be negligible to overall results.
    </li>
    <li>
        <b>Oversampling factor:</b> Oversample master and slave(s) with this factor before computing the complex interferogram
        for the peak estimation. This factor has to be a power of 2. 2 is default, and with this factor the filter is
        able to estimate the peak for frequency shifts larger than half the bandwidth. A factor of 4 for example might
        give a better estimate, since the interval between shifts that can be estimated is in that case halfed
        (fixed FFT Window Length).
    </li>
</ul>

<h4>Source bands:</h4>&nbsp;&nbsp;
<p> Source Bands are set of coregistered bands of the complex product.</p>

<h4>Output bands:</h4>&nbsp;&nbsp;
<p> Output Bands are set of bands with spectras filtered in range direction.</p>


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